梅尔曼–瓦格纳定理
(重定向自Mermin–Wagner定理)
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在量子场论和统计力学中,梅尔曼–瓦格纳定理(Mermin–Wagner定理,或称梅尔铭-瓦格纳-霍亨贝格定理、梅尔铭-瓦格纳-別列津斯基定理、科勒曼定理)阐述了维度d ≤ 2的场论没有自发对称破缺(要不然无质量的南部玻色子会有无限的相关函数)。
概览
若 φ 是高斯自由场(一种纯量场),m是质量,维度d=2;传播子是:
若m=0,
因为高斯定律,
若,,所以一维或二维的纯量场没有明确定义的平均值。
参见墨西哥帽模型。
XY模型的相变
d=2的O(2)模型没有自发对称破缺,但是有别列津斯基-科斯特利茨-索利斯相变。
(量子相變不受影响。)
两相是:
1、
2、冪定律
(a ≪ r ≪ ξ
a 是晶格常數
历史
2D晶体
限制
参考文献
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